PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(2^267149+2562)/280420Stefano Morozzi01/2020
975221321^5908+5908^2132180411Hans Havermann02/2020
9753(13100^19531-1)/1309980411Serge Batalov08/2020
97542^267116-45995980410Enzo Doria06/2015
975538715!2+880406Robert Price01/2015
975619579^12786+12786^1957980406Hans Havermann02/2020
9757(2^267017+1)/380380H.&R. Lifchitz09/2000
9758(2^267006+1134)/280377Stefano Morozzi01/2020
975924273^2048+2048^2427380376Hans Havermann01/2020
9760(2^266989+734)/280372Stefano Morozzi01/2020
9761(2^266989+1850)/280372Stefano Morozzi01/2020
9762(13427^19471-1)/1342680372Serge Batalov08/2020
97632^266968-4580366Lelio R Paula05/2012
9764(2^266967+3974)/280365Stefano Morozzi01/2020
976520^61768-6380363Lelio R Paula01/2016
9766(6253^21169-1)/625280356Serge Batalov08/2020
9767(14005^19381-1)/1400480355Serge Batalov08/2020
97682^266920-11296780351Enzo Doria06/2014
9769(2^266910+2394)/280348Stefano Morozzi01/2020
9770(2^266899+1994)/280345Stefano Morozzi01/2020
97718*10^80342+8780343Robert Price10/2017
9772(10^80363+1)/1186613600417422195087690646380335Anonymous10/2020
9773(2^266861+890)/280333Stefano Morozzi01/2020
977412^74428-1380322Lelio R Paula11/2015
9775(2^266810+2718)/280318Stefano Morozzi01/2020
9776(2^266800+2886)/280315Stefano Morozzi01/2020
9777(6163^21187-1)/616280291Serge Batalov08/2020
97782^266680+2780279Lelio R Paula05/2012
9779(232*10^80264+17)/380266Robert Price04/2021
97802^266630-13180264Lelio R Paula05/2012
9781(2^266627+1278)/280263Stefano Morozzi01/2020
97822^266598+7681980254Enzo Doria05/2016
978324463^1908+1908^2446380253Hans Havermann01/2020
97842^266587+188063380251Enzo Doria10/2016
9785(2^266570+3942)/280246Stefano Morozzi01/2020
97862^266541-11004980237Enzo Doria04/2014
978738635!2-880222Robert Price06/2015
9788(2^266465+986)/280214Stefano Morozzi01/2020
97893^168111+168111^3-180210Robert Price04/2014
9790(2^266447+758)/280209Stefano Morozzi01/2020
97912^266443+51380208Lelio R Paula07/2013
9792(26*10^80200+61)/380201Robert Price06/2017
97932^266412-10991380199Enzo Doria04/2014
9794(10223*2^266417+1)/4509180199Lelio R Paula06/2014
97952^266413-469380199Yves Minet05/2019
9796(13737^19381-1)/1373680193Serge Batalov08/2020
979713^71988+6680191Lelio R Paula11/2015
979811^77002-432080190Enzo Doria01/2013
979919839^11012+11012^1983980187Hans Havermann03/2020
980118^63879-1380186Lelio R Paula11/2015
9800(2^266371+1814)/280186Stefano Morozzi01/2020
98022^266368-11229580185Enzo Doria06/2014
980319217^14880+14880^1921780185Hans Havermann03/2020
9804(3^168050+5)/102145480175Lelio R Paula10/2012
9805(2^266324+1386)/280172Stefano Morozzi01/2020
9806(22*10^80167+41)/980168Robert Price02/2015
9807(2^266308+1618)/280167Stefano Morozzi01/2020
9808(34*10^80162-43)/980163Ray Chandler12/2010
9809(2^266276+762)/280157Stefano Morozzi01/2020
9810(38*10^80150-11)/980151Robert Price05/2015
9811(598*10^80149-31)/980151Robert Price02/2017
981219^62678-8080150Lelio R Paula12/2015
9813(559^29173-1)/55880148Serge Batalov08/2020
981410^80139+3234380140Patrick De Geest02/2011
981510^80139-980139Alexander Gramolin01/2011
98163^167955-10680135Lelio R Paula12/2015
981720545^7944+7944^2054580127Hans Havermann04/2020
981818876^17569+17569^1887680124Hans Havermann03/2020
9819(2^266137+3782)/280115Stefano Morozzi01/2020
9820(2^266121+3846)/280111Stefano Morozzi01/2020
9821(22*10^80098+47)/380099Robert Price06/2021
982222752^3313+3313^2275280093Hans Havermann03/2020
9823(197*10^80089-11)/380091Robert Price10/2017
98242^265998+7555980074Enzo Doria04/2016
9825(2^265999+3290)/280074Stefano Morozzi01/2020
98262^265969-10980180065Enzo Doria04/2014
9827(2^265956+3378)/280061Stefano Morozzi01/2020
9828(185*10^80051-11)/380053Robert Price10/2020
98292^265888-11275780041Enzo Doria06/2014
9830(24847^18211-1)/2484680038Serge Batalov08/2020
98312^265809+170180017Lelio R Paula07/2013
9832gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
983319807^10954+10954^1980780012Hans Havermann04/2020
98343^167687-10480008Lelio R Paula02/2015
983511^76826-579080007Enzo Doria01/2013
983610^80000+8573180001Patrick De Geest10/2009
983710^80000-716980000Patrick De Geest09/2009
983810^79999+2239980000Patrick De Geest09/2009
983910^79999-7487379999Patrick De Geest09/2009
98403^167668+5879998Lelio R Paula02/2015
9841(59*10^79995+391)/979996Robert Price03/2021
9842(2^265728+3742)/279992Stefano Morozzi01/2020
984318780^18137+18137^1878079976Hans Havermann04/2020
984419190^14709+14709^1919079976Hans Havermann04/2020
9845155^36506-279961Lelio R Paula10/2017
9846(2^265621+3882)/279960Stefano Morozzi01/2020
98482^265612+425779958Lelio R Paula07/2013
9847(2^265613+1470)/279958Stefano Morozzi01/2020
98495*3^167577+479956Lelio R Paula06/2014
9850(9179*2^265593-1)/979955Lelio R Paula04/2015
985110^79939-700000179939Robert Price06/2021
98526^102723-4379935Lelio R Paula04/2015
985321052^6261+6261^2105279927Hans Havermann03/2020
985411^76748-336079925Enzo Doria12/2012
985519430^12981+12981^1943079922Hans Havermann03/2020
9856(2^265490+870)/279921Stefano Morozzi01/2020
9857(13*2^265498-1)/18711979919Lelio R Paula02/2014
9858(2^265438+3978)/279905Stefano Morozzi01/2020
9859(2^265409+1250)/279896Stefano Morozzi01/2020
98602^265399-10985579894Enzo Doria04/2014
9861(2^265380+3930)/279888Stefano Morozzi01/2020
9862(20^61403-1)/1979886Paul Bourdelais03/2010
9863(2^265368+2970)/279884Stefano Morozzi01/2020
986418^63635+5979880Lelio R Paula02/2015
9865(11*10^79867-107)/379868Robert Price11/2016
98663^167375+8079859Lelio R Paula02/2015
98675^114240-1448679851Enzo Doria02/2013
986849^47238+4879842Norbert Schneider07/2014
98692^265212-377979837Yves Minet04/2017
9870(2^265201+2790)/279834Stefano Morozzi01/2020
987191^40746+40746^9179824Norbert Schneider12/2014
9872(68*10^79813-257)/979814Robert Price06/2017
9873(13063^19391-1)/1306279811Serge Batalov08/2020
9874(5*2^265118-1)/6179808Lelio R Paula02/2014
9875(2^265102+1462)/279804Stefano Morozzi01/2020
98762^265074+2842579796Lelio R Paula07/2013
98772^265072+118579795Lelio R Paula07/2013
9878p(16682)#/2-12879771Robert Price05/2017
9879(2^264994+1714)/279771Stefano Morozzi01/2020
98813^167167-3479759Robert Price11/2013
9880(2^264952+3258)/279759Stefano Morozzi01/2020
988212^73906+2979758Lelio R Paula02/2015
98832^264934+25579754Lelio R Paula07/2013
98844*10^79729-8779730Robert Price03/2017
98852^264846-11170179727Enzo Doria05/2014
98862^264831-11204179723Enzo Doria06/2014
98872^264816-45579718Yves Minet03/2012
9888(55*10^79711+89)/979712Robert Price09/2017
988947^47667-4679704Theodore Burton02/2007
989013^71547+9679700Lelio R Paula03/2015
98912^264752-11288379699Enzo Doria06/2014
9892(2^264748+1978)/279697Stefano Morozzi01/2020
9893(185*10^79694-11)/379696Robert Price10/2020
98942^264732+13379693Lelio R Paula05/2012
98958*3^167010+779685Lelio R Paula06/2014
989642^49087-4179681Norbert Schneider06/2014
9897(26*10^79678-119)/379679Robert Price07/2016
98982^264683-2179678Lelio R Paula05/2012
98997^94279+1879675Lelio R Paula02/2015
99002^264655-12779670Lelio R Paula02/2012
9901(2^264658+3102)/279670Stefano Morozzi01/2020
9902(2^264637+1682)/279664Stefano Morozzi01/2020
99032^264597-45904379652Enzo Doria05/2015
9904(21*2^264566+1)/579643Lelio R Paula10/2012
99052^264536+187002179634Enzo Doria05/2016
9906(17*2^264512-1)/35979625Lelio R Paula02/2014
990719957^9762+9762^1995779620Hans Havermann03/2020
99082^264477-10978379616Enzo Doria04/2014
990918^63419-133379609Enzo Doria03/2013
991013^71451-3679593Lelio R Paula03/2015
991123314^2593+2593^2331479590Hans Havermann03/2020
99123*10^79586+3179587Robert Price06/2021
9913(2^264410-5)/12800260912179585Lelio R Paula10/2012
991419^62234+9079582Lelio R Paula03/2015
9915(2^264276+2866)/279555Stefano Morozzi01/2020
991612^73714+4979551Lelio R Paula02/2015
9917(2^264213+1442)/279536Stefano Morozzi01/2020
9918(3*2^264184-1)/143333979522Lelio R Paula02/2014
9919(2^264160+1590)/279520Stefano Morozzi01/2020
9920(29*10^79510-107)/379511Robert Price08/2020
9921(9363^20021-1)/936279508Serge Batalov08/2020
99222^264103-11253179503Enzo Doria06/2014
992319^62170+7879501Lelio R Paula03/2015
9924((10^(4*19875)-1)/9999)*18880+179501Matt Stath01/2021
992511^76340-258079500Enzo Doria12/2012
9926(2^264084+858)/279497Stefano Morozzi01/2020
9927(5652^21187-1)/565179495Serge Batalov08/2020
9928(23*10^79492-11)/379493Robert Price10/2015
9929((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
99302^264060-11213379490Enzo Doria06/2014
9931((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
993220158^8775+8775^2015879488Hans Havermann02/2020
99339^83298+6^83298-2^8329879487Mike Oakes08/2010
993418^63319+3579483Lelio R Paula02/2015
9935(10011^19867-1)/1001079474Serge Batalov08/2020
99362*10^79468+7779469Robert Price08/2020
993722479^3428+3428^2247979465Hans Havermann04/2020
993838303!2+25679461Robert Price01/2015
9939(29*10^79445+61)/979446Robert Price04/2015
99402^263902-19579443Lelio R Paula05/2012
99413^166499-11269679441Enzo Doria06/2014
994211^76279-276079437Enzo Doria12/2012
994318907^15894+15894^1890779433Hans Havermann03/2020
99446^102077-2579432Lelio R Paula03/2015
99452^263852-101779428Lelio R Paula07/2013
99462^263842-3379425Lelio R Paula05/2012
9947(2^263814+3582)/279416Stefano Morozzi01/2020
994812^73584-5579411Lelio R Paula02/2015
9949(2^263783+3558)/279407Stefano Morozzi01/2020
99502^263772-18579404Lelio R Paula05/2012
9951(15^67489+1)/1679373Paul Bourdelais03/2010
99522^263664+1501579371Lelio R Paula07/2013
9953(2^263643+1206)/279365Stefano Morozzi01/2020
9954(2^263642+3082)/279364Stefano Morozzi01/2020
9955(3319^22541-1)/331879364Serge Batalov08/2020
995610^79362+3^7936379363Mike Oakes06/2010
9957(2^263591+2910)/279349Stefano Morozzi01/2020
9958(2^263589+1922)/279348Stefano Morozzi01/2020
9959Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
99603^166262+4479328Lelio R Paula02/2015
99614*10^79327-6379328Robert Price12/2016
99622^263486+51379318Lelio R Paula07/2013
9963(2^263458+1282)/279309Stefano Morozzi01/2020
9964(2^263456+1558)/279308Stefano Morozzi01/2020
99652^263448-51950979306Paul Bourdelais03/2013
9966(18926^18541-1)/1892579297Serge Batalov08/2020
996769153^16384+279296Matt Stath01/2019
996821^59971-20^5997179295Robert Price05/2012
99692^263372+12379283Lelio R Paula05/2012
9970(2^263366+1974)/279281Stefano Morozzi01/2020
997117^64429+8479277Lelio R Paula03/2015
997211^76124-1143079275Enzo Doria12/2012
997319294^12845+12845^1929479274Hans Havermann03/2020
9974(206*10^79268-17)/979270Robert Price03/2017
997513^71157+1879265Lelio R Paula03/2015
9976(11*10^79262-23)/379263Robert Price09/2021
99772^263297+6583579261Lelio R Paula07/2013
997819^61980-1879258Theodore Burton12/2005
9979(2^263259+2970)/279249Stefano Morozzi01/2020
99802*10^79242+9379243Robert Price07/2016
9981(2^263226+1074)/279239Stefano Morozzi01/2020
9982(88^40751-1)/8779238Paul Bourdelais08/2017
9983(103*29^54179-39)/479233Curtis Bright05/2015
99849^83024-83024^979226Norbert Schneider08/2017
998517^64382-2679219Lelio R Paula03/2015
99867^93733-7479214Lelio R Paula02/2015
998715^67352+3879213Lelio R Paula02/2015
99882^263135-11023579212Enzo Doria05/2014
9989(2^(8768)*3^(77475)-1)^(2)-(2^(8768)*3^(77475)-1)+4179209Tapashree & Jainam08/2021
9990(2^263080+3658)/279195Stefano Morozzi01/2020
99912^263044+425779185Lelio R Paula07/2013
9992(2^263039+3554)/279183Stefano Morozzi01/2020
99942^263032+8751779181Yves Minet11/2010
99936^101755+9579181Lelio R Paula03/2015
9995(2^263010+1738)/279174Stefano Morozzi01/2020
99964^131497-3^13149779170Jean-Louis Charton05/2004
99975*7^93674+879165Lelio R Paula10/2014
9998(2^262939+1326)/279153Stefano Morozzi01/2020
9999(2^262941+926)/279153Stefano Morozzi01/2020
10000lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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